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Diffusing particles with electrostatic repulsion
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  • Published: 01 April 1997

Diffusing particles with electrostatic repulsion

  • Emmanuel Cépa1 &
  • Dominique Lépingle1 

Probability Theory and Related Fields volume 107, pages 429–449 (1997)Cite this article

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Summary.

We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles \(N\) goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as \(N \uparrow \infty\)) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE.

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Authors and Affiliations

  1. MAPMO, Université d'Orléans, BP 6759, F-45067, Orléans Cedex 2, France

    Emmanuel Cépa & Dominique Lépingle

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  1. Emmanuel Cépa
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  2. Dominique Lépingle
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Received: 5 August 1996 / In revised form: 17 October 1996

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Cépa, E., Lépingle, D. Diffusing particles with electrostatic repulsion. Probab Theory Relat Fields 107, 429–449 (1997). https://doi.org/10.1007/s004400050092

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  • Published: 01 April 1997

  • Issue Date: April 1997

  • DOI: https://doi.org/10.1007/s004400050092

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  • Mathematics Subject Classification (1991): 60K35, 60F05, 60H10, 60J60
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